Stationary cocycles and Busemann functions for the corner growth model

Understand

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d.

• weights on the vertices, outside of the class of exactly solvable models.
• Stationary cocycles are constructed for this percolation model from queueing fixed points.
• These cocycles serve as boundary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity.